475. Heaters
1. Description
Winter is coming! During the contest, your first job is to design a standard heater with a fixed warm radius to warm all the houses.
Every house can be warmed, as long as the house is within the heater’s warm radius range.
Given the positions of houses and heaters on a horizontal line, return the minimum radius standard of heaters so that those heaters could cover all houses.
- Notice that all the heaters follow your radius standard, and the warm radius will the same.
2. Example
Example 1:
Input: houses = [1,2,3], heaters = [2]
Output: 1
Explanation: The only heater was placed in the position 2, and if we use the radius 1 standard, then all the houses can be warmed.
Example 2:
Input: houses = [1,2,3,4], heaters = [1,4]
Output: 1
Explanation: The two heater was placed in the position 1 and 4. We need to use radius 1 standard, then all the houses can be warmed.
Example 3:
Input: houses = [1,5], heaters = [2]
Output: 3
3. Constraints
- 1 <= houses.length, heaters.length <= $3 * 10^4$
- 1 <= houses[i], heaters[i] <= $10^9$
4. Solutions
Sorting && Binary Search
m = houses.size(), n = heaters.size()
Time complexity: O((m + n)logn)
Space complexity: O(logn)
// never change the input
class Solution {
public:
int findRadius(const vector<int> &houses, vector<int> heaters) {
sort(heaters.begin(), heaters.end());
int result = 0;
for (int i = 0; i < houses.size(); ++i) {
int shortest_heater_distance = find_shortest_heater_distance_(houses[i], heaters);
result = max(result, shortest_heater_distance);
}
return result;
}
private:
int find_shortest_heater_distance_(int house, const vector<int> &heaters) {
int result = INT_MAX;
for (int left = 0, right = heaters.size(); left < right;) {
int mid = left + (right - left) / 2;
result = min(result, abs(house - heaters[mid]));
heaters[mid] < house ? left = mid + 1 : right = mid;
}
return result;
}
};
Sorting && Two Pointers
m = houses.size(), n = heaters.size()
Time complexity: O(mlogm + nlogn)
Space complexity: O(logm + logn)
class Solution {
public:
int findRadius(vector<int> houses, vector<int> heaters) {
sort(houses.begin(), houses.end());
sort(heaters.begin(), heaters.end());
int result = 0;
for (int i = 0, left = 0, right = 0; i < houses.size(); ++i) {
for (; right < heaters.size() - 1 && heaters[right] < houses[i]; ++right)
;
left = max(0, right - 1);
result =
max(result,
min(abs(houses[i] - heaters[left]),
abs(houses[i] - heaters[right])));
}
return result;
}
};